Early exercise policies of American floating strike and fixed strike lookback options

Abstract

Using appropriate similarity transform, we present the partial differential equation formulation of both floating strike and fixed strike American lookback option models. We examine the early exercise policies of the floating strike and fixed strike American lookback options, while the realized extrmum of the asset price can be monitored continuously or discretely. The characterizations of the optimal exercise prices of American lookback options are also discussed. For the numerical valuation of the American lookback options, several approaches for deriving efficient and accurate numerical results are addressed.